Equalization

to Open your Eye

吳瑞北, Ruey-Beei Wu

Rm. 340, Department of Electrical Engineering

E-mail: rbwu@ew.ee.ntu.edu.tw

url: http://cc.ee.ntu.edu.tw/~rbwu

S. H. Hall & H. L. Heck, High-Speed Digital Designs, ch. 12. 1

R. B. Wu

What will you Learn?

• How eye diagram is defined?

• How eye diagram is related to ISI?

• How to construct eye diagram from impulse

response?

• How to make eye diagram better?

• General concept for better eye?

• Do you know typical examples to make eye

diagram better.

2

R. B. Wu

Contents

• Max. Data Transfer Capacity

• Introduction

– Linear Time Invariant Systems

– ISI and Eye-Diagram

– Equalization Mechanism

• Continuous Time Equalization

• Discrete Time Equalization

– Discrete Time Linear Equalizer (DTLE)

– Decision Feedback Equalizer (DFE)3

R. B. Wu

Shannon’s Capacity Theorem

• Upper limit on data transfer rate:

• Max. # bits/symbol

4

2

D S B

S BW

S: symbols/sec;

B: # bits/symbol

BW: bandwidth in hertz

2

1log 1

2

S

N

PB

P

PS: avg. signal power

PN: noise power

SNR=PS/PN , signal to

noise ratio

2log 1D BW SNR

R. B. Wu

• Impulse response

• Convolution

• Superposition

FFT

Insertion loss S

parameters

(complex)

Insertion loss S

parameters

(Magnitude

and phase)FFT

Impulse response

Frequency response

Linear Time-Invariant (LTI) Systems

5

R. B. Wu

Tx symbol

(mirror)

Impulse

response

Pulse response

LTI Property: Convolution

6

R. B. Wu

Tx symbol

…000010011100…

In Out

Response to pattern 100111

LTI Property: Superposition

7

R. B. Wu

Effects of Larger Channel Length

• Notice the effect on the lone narrow bit verses the wider pulse that is representative of multiple bits.

• The lone pulse looks more and more like a runt as the channel length increases

Tx

channel

Rx

channelRx

channel Rx

channel Rx

8

R. B. Wu

Inter-Symbol Interference (ISI)Frequency dependant loss causes data dependant jitter

which is also called inter symbol interference (ISI).

The cannel BW limit degrades the signal quality.

It depends on line-length, data rate and substrate material

on board typically.

9

R. B. Wu

ISI (Inter-Symbol Interference)

• Frequency dependant loss causes data dependant jitter which is also called inter symbol interference (ISI).

• In general the frequency dependant loss increase with the length of the channel.

• The high frequencies associated with a fast edge are attenuated greater than those of lower frequencies.

– The wave received at the end of a channel looks as if the signal takes time to charge up. If we wait long enough, it reaches the transmitted voltage. If not long enough and a new data transition occurs, the previous bit look attenuated.

– Hence a stream of bits will start or finish the charge cycle at different voltage point which will look to the observer as varying amplitudes for various bits in the data pattern.

10

R. B. Wu

Eye-Diagram

11

R. B. Wu

Eye-Diagram

14

R. B. Wu 15

Construction of Eye-Diagram

Input Signal Output SignalSystem Response

H( f )

h( t )

orUsing pseudo-random

bit sequence (PRBS) as

input signal is time-

consuming to obtain eye

diagram, especially for

complicated systems.

R. B. Wu 16

Impacts on SI 10

12.5

15

17.5

(GHz)

2.5

5.0

7.5

10

12.5

15

17.5

(GHz)

2.5

5.0

7.5

Chip A

Chip B

Eye Diagram Variation vs. Physical Parameter Variation

How to Compensate the Degraded Eye-Diagram Performance

As for lossy tx-line, there are two issues worth researching :

(1). Reflection noise,

(2). Crosstalk,

(3). Lossy effect,

(4). Ground Bounce.

Eye Mask

R. B. Wu

How to Have Better Eye?

• Solution: Boost the amplitude of the first bit.

• Key concept: we drive to a higher voltage at the

high frequency component and a lesser voltage at

lower frequency.

Transition bit

17

R. B. Wu

Discrete Time Equalization

• Normally the max current is supplied on the

transition bit and reduces on subsequent bits.

• If we reference to the transition bit to a

transmitter, it is commonly called “de”-emphasis.

The low-freq bits are attenuated.

• If we talk about the non-transition bit in reference

to a receiver or passive network, we might call this

“pre”-emphasis. The high-freq bits are amplified.

• Although the two may be considered the same, the

former is used more commonly.

18

R. B. Wu

Continuous Time Equalization (1/2)

• Given that the channel has a complex loss versus

frequency transfer function, Hch(w)

• FFT of an input signal multiplied by the frequency

transfer function is the response of the channel to

that input in the frequency domain. tx(t)Tx(w)

• If we take IFFT of the previous cascade response,

we get the time-domain signal of the channel

output, i.e., rx(t)=IFFT(Tx(w)*Hch(w))

19

R. B. Wu

Continuous Time Equalization (2/2)

• Given the response of the output: Tx(w)*Hch (w)

• If we multiply this product by 1/ Hch (w), look what

happens? The result is Tx(w).

• The realization of 1/ Hch (w) is called equalization

and my be achieved number of ways.– If applied to the transmitter, it is called transmitter

equalization. This approximated by the boost we referred

to earlier.

– If it is applied at the output of the channel, it is called

receiver equalization.

– If done properly, the results are the same but cost and

operation factors may favor one over the other.

20

R. B. Wu

Bitwise Conceptualization

Hch(f)

Frequency

0dB

1/Hch(f) Ideal equalizationdB

Bitwise equalization

• Approximation based

on bit transitions

• More bits may better

approximate 1/h(f)

21

Continuous Time Equalizers

22

R. B. Wu

• The passive CLE is a

high pass filter.

• Low frequency

components are

attenuated.

• The filter can be located

anywhere in the

channel, and can be

made of discrete

components, integrated

into the silicon, or even

built into cables or

connectors.

100fF

20fF

RHP=5-40 k

RL=2.5-20 k

100

Passive CTLE

23

R. B. Wu

Passive Cont. Linear Equalizer

• The passive CLE is a high pass filter.

• Low frequency components are attenuated.

• Amplification of high frequency components is possible, too.

• The filter can be made of discrete components, integrated into the silicon, or even built into cables or connectors.

22

22

21 CfRj

RZ

321

3

ZZR

ZfH CLE

33

33

21 CfRj

RZ

R1 = 100

C2 = 100fF

R2 = 5k

R3 = 2.5k C3 = 20fF

R. B. Wu

6dB - Rule of Thumb

• 6-dB loss is sufficient to completely close the eye of a

sinusoid, independent of swing and frequency.

25

R. B. Wu

Demonstrative Example

• CTLE design:

RL=2.5k, RHP=5k.

• Variation reduced by 5dB

• 38.1cm diff. line on PCB

with 500mV @ 10Gbps

26

Eyeshift 44 %

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100300

240

180

120

60

0

60

120

180

240

300

vo

ltag

e (

mV

)

time (ps)

Eyeshift 48 %

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100150

120

90

60

30

0

30

60

90

120

150

vo

ltag

e (

mV

)

time (ps)

Eye mask : 20 mV x 50 ps

R. B. Wu

Verification on Pulse Stream

Un-equalized:

Max. range:

-210 ~ 200mV

Min swing:

-5 ~ 5 mV

Equalized:

Max range;

-105 ~ 125mV

Min swing:

-20 ~ 30 mV

27

R. B. Wu

Transfer Function for PCB-CTLE System

0 1 2 3 4 5 6 7 8 9 1030

27

24

21

18

15

12

9

6

3

0

frequency (GHz)

Mag

nitu

de(d

B)

Passive Continuous Linear Equalizer

CTLE

PCB

PCB+CTLE

-16.0 dB

-21.0 dB

Closed eye

Closed eye

The passive equalizer doubles the usable spectrum. 28

R. B. Wu

Compensation based on RLC Filter

W. Humann, “Compensation of Transmission Line Loss for Gbit/s Test on

ATEs,” 2002 Int. Test Conf, 7-10 Oct. 2002, Pages:430 - 437 29

R. B. Wu

Theory - no reflection design

10-2

10-1

100

101

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Create of Compensation Curve

frequency (GHz)

att

en

uati

on

(d

B)

ideal compensation curve

S21 of lossy line

DC loss target

S11=S22=0

2 2

1 1 2 02R R R Z

2

0L Z C

S21 = DC loss of compensation ckt.

0 121

0 1

1 2

1 2

c

c

Z R jS

Z R j

w w

w w

, where

1c

LCw ,

At DC : 0 121

0 1

1

1

Z RS

Z R

R1

R3

R2

L

C

1 3R R

30

R. B. Wu

Active CTLE

1 3

1 1 3 2

OP equations: 0;

( )in out in

i i v v

R Rv v v

R j C R Rw

2 3

1 1

1( ) 1

1 1

R RH

R Cw

w

31

R. B. Wu

Reflection Enhanced Equalizer

W.-D. Guo, F.-N. Tsai, G.-H. Shiue, & R.-B. Wu, “Reflection enhanced compensation of lossy traces for best

eye-diagram improvement using high-impedance mismatch,” IEEE Trans. Adv. Packag., Aug. 2008

32

Rx

Rin ≈ ∞

VO

Metal : Copper

εr = 4.4tan δ = 0.022

0.6 mm

1.1 mm1.34 mil

Microstrip line( Z0 ≈ 50Ω, Length : 30" )

+ VS

RS=50Ω

Tx ГS ГL

RL=

50Ω

Vo

50Ω

Lc

Main line

Rx

Inductance Insertion

Step response for lossless line

(gray : w/o inductance;

black : w/ inductance)

Bigger positive reflection for

high-frequency component

High-Impedance Line Insertion

Vo

50Ω

Main line

Rx, h hZ l

0( )hZ Z

Step response for lossless line

(gray : w/o high-Z0 line;

black : w/ high-Z0 line)

Positive

reflectionNegative

reflection

round

trip

5Gbps PRBS,

tr = 50ps,

Vin = 0.8V

R. B. Wu 33

Compensation Principle

Lc = 0nH

Lc = 2.5nH

Lc = 5nH

Lc = 8nH

Lc = 10nH

H( f )

0 1 2 3 4 5Frequency (GHZ)

-16

-12

-8

-4

0

Volt

age

tran

smis

ssio

n c

oef

fici

ent

|VT( f )|

(d

B)

10 12 14 16 18 20(ns)-200

0

200

400

600(mV) Waveform at Lc = 8nH

Vo

50Ω

Lc

Main line

Rx

( )( ) ( ) 1 ( )

2

S

O L

V fV f H f f

0

2

0

( ) 1 ( )( ) ( )

1 ( ) ( ) ( )

L

O S

S S L

H f fZV f V f

Z R H f f f

( ) 2 ( ) ( )T O SV f V f V fDefine

0 4 8 12 16 20Inductance, L (nH)

200

240

280

320

360

400

Eye

hei

gh

t (m

V)

140

150

160

170

180

190

200

Eye

wid

th (

ps)

c

Height (mV)

Width (ps)

Original

Optimum

Improved

253

373

30%

188

195

3.5%(ΔV/Vin) (ΔW/Win)

Input Signal :

data rate = 5 Gbps &

rise time = 50 ps

R. B. Wu 34

Despite the compensation method can help improve the system performance,

an ultimate will exist because the well-compensated |VT( f )| is still “lossy”.

Before compensation After compensation

(20 in. up)

(14 in. up)

(8 in. up)

Max. Usable Length Enhancement

R. B. Wu

Experimental Verification (1/2)

35

R. B. Wu 36

Experimental Verification (2/2)

(38inch)

Vo

50Ω

Lc

Main line

Rx

Vo

50Ω

Main line

Rx, h hZ l

0( )hZ Z

,10

20

c

h

L nH

l mm0.6mm

Metal : Copper

εr = 4.4tan δ = 0.02

1.1mm1mil

Original Lossy Line Inductance Compensation High-Z0 Line Compensation

Simul.

Meas.

Volt

age

[50 m

V/d

iv]

Time [40 ps/div]

300 mV

184 ps

Volt

age

[50 m

V/d

iv]

Time [40 ps/div]

305 mV

188 ps

Volt

age

[50 m

V/d

iv]

Time [40 ps/div]

140 mV

158 ps

0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time (ps)

Voltage (

V)

146mV

184 ps

0 100 200 300 400

0

0.1

0.2

0.3

0.4

Time (ps)

Voltage (

V)

313mV

194 ps

0 100 200 300 400

0

0.1

0.2

0.3

0.4

Time (ps)

Voltage (

V)

305mV

190 ps

Discrete Time Equalizers

37

R. B. Wu

Transmitter Equalization

• It becomes clear what a tap is when we look at lone bit (data pattern ~ …0001000000…)

This is called 2

tap equalization

Tap1

Also called cursor.

We will explore the whole

concept of cursors later

Tap 2

VshelfVswingCommonly the

2 Tap de-emphasis

spec in dB and is

-20*log(Vshelf/Vswing)

Vtap138

R. B. Wu

Tap Coefficients

• Taps are normalized so that absolute sum of the cursor tap and the pre and post cursor taps is equal to 1 with the base equal to zero. The reason will become clear later.

• Lets take the last example where de-emphasis is defined as -6 dB. This would correspond to tap1=0.75 and tap2=0.25. These are called tap coefficients.

Tap1: This tap is

called the cursor

tap2

base = 0

39

R. B. Wu

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 Bits

0 0 0 0 0 0 0 ¾ ½ ½ -¼ 0 0 ¾ ½ ½ -¼ 0 0 0 0 Value

S

0 0 0 0 0 0 1 0 0 0 0 0 0.75

0.0-0.25

Superposition through Caps

40

R. B. Wu

Resultant Waveform

• Observe that Vshelf is ½ and Vswing is 1.

• For 2 tap systems we call this 6dB de-emphasis 20*log(0.5)

• 20*log(Vshelf/Vswing) is not a robust and easily expandable

specification but common used in the industry and call the

transmitter de-emphasis spec,

• A more robust way would be to spec tap coefficients which we

will take a bit more about later

Renormalize to 1 peak to peak: Value-1/4-¼ -¼ -¼ -¼ -¼ -¼ -¼ ½ ¼ ¼ -½ -¼ -¼ ½ ¼ ¼ -½ -¼ -¼ -¼ -¼ renorm

½1

0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 Bits

0 0 0 0 0 0 0 ¾ ½ ½ -¼ 0 0 ¾ ½ ½ -¼ 0 0 0 0 Value

41

R. B. Wu

Transmit Equalization (a.k.a. Pre-Emphasis)

• Isolated bits or rapidly alternating 0s/1s don’t

build up to the full swing at the receiver in a

lossy channel.

• This gives a closed eye at the receiver.

Pre-emphasis adjusts the magnitude of

the transmitter output based on prior bit

values.

Often done by attenuating successive

bits (“de-emphasis”).

This reduces the maximum swing, but

produces an open eye.

No

n-E

qu

aliz

ed

Eq

ual

ized

0 1 2 3 4 5 6 7 8150

90

30

30

90

150

210

270

330

390

450

time [ns]

vo

lta

ge [

mV

]

Waveforms

0 1 2 3 4 5 6 7 850

10

70

130

190

250

310

370

430

490

550

time [ns]

vo

lta

ge [

mV

]

Waveforms

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 20075

115

155

195

235

275

315

355

395

435

475

time [ps]

vo

lta

ge

[mV

]

Rx Eye Diagram

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 20050

72.5

95

117.5

140

162.5

185

207.5

230

252.5

275

time [ps]

vo

lta

ge

[mV

]

Rx Eye Diagram

R. B. Wu

The outputs from the weights are summed to produce the transmitter output.

The number of taps depends on the length of the channel relative to the unit interval of the data.

Pre-Emphasis Circuit

• DLEs use finite impulse response (FIR) filters.

• The input stream propagates thru a series of delay lines.

– Each line typically has a delay of one unit interval.

• The input signal is sampled between each delay line and multiplied by a weighting factor (Ck).

– Negative subscripts compensate “precursor” ISI, positive for “postcursor” ISI.

D D D

C-1

C0

C1

C2

S yk

xk

43

R. B. Wu

Tx Pre-emphasis Example Pulse arrives filter input & is multiplied by C-1,

generating a precursor pulse of -50 mV

amplitude and 1 ns duration.

1 ns later, the pulse is at tap 3 tap & gets

weighted with C1, generating the first postcursor

pulse (-100 mV amplitude, 1 ns duration).

1 ns later, the reaches the final tap, is multiplied

by C2, creating the +50 mV, 1 ns 2nd postcursor

pulse.

C-1 C0 C1 C2

T T T

S yk

xk

3 42

After 1 ns delay, pulse appears at tap 2 &

is multiplied by C0, generating the 400

mV, 1 ns cursor pulse.

2

400 mV 3

-100 mV

4

50 mV

1

-50 mV

1

600 mV

1 ns

44

R. B. Wu

Tx Pre-emphasis

Pulse arrives filter input & is multiplied by C-1,

generating a precursor pulse of -50 mV amplitude

and 1 ns duration.

1 ns later, the pulse is at tap 3 tap & gets

weighted with C1, generating the first postcursor

pulse (-100 mV amplitude, 1 ns duration).

1 ns later, the reaches the final tap, is multiplied

by C2, creating the +50 mV, 1 ns 2nd postcursor

pulse.

After 1 ns delay, pulse appears at tap 2 &

is multiplied by C0, generating the 400

mV, 1 ns cursor pulse.

1

2

3

4

+

T

4 ns

400 mV

-100 mV

R. B. Wu

To derive the frequency domain

transfer function apply the time shift

property of the Fourier transform,

w(t-T) ↔ W(f )e- j2fT, to the time

domain filter response w/ T = unit

interval.

N=2

C0=.75

C1=-0.2

C2=-0.05-7

-6

-5

-4

-3

-2

-1

0

0 2 4 6 8 10

f [GHz]

|H(f

)| [

dB

]

6.4 Gb/s

10 Gb/s

12.8 Gb/s

FIR Filter Response

where ck=tap Coefficient, k=tap number (0=cursor), N=# of taps

post

pre

n

nn

ncnkxky

Time Domain

post

pre

n

nk

Tkfj

k ecfH 2)(

Frequency Domain

46

R. B. Wu

Rx Discrete Time Linear Equalizer (DLE)

• The receive-side DLE

works just like the

transmitter pre-emphasis

circuit.

• The only difference is that

it samples the incoming

analog voltage.

• Uses a “sample & hold”

circuit at the input, which

provides the input signal

stream to the FIR.

C-1

C0

C1

C2

D D D

S yk

xk

47

R. B. Wu

-2 -1 0 1 2 3 4 5time (UI)

-3

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

volt

ag

e (V

)

Discrete Linear Equalizer Design

• Conceptually, we want

the receiving equalizer to

generate a set of

canceling “echoes”

Since we sample at

predetermined points,

the equalizer design

can be straightforward,

but will only cancel ISI at the sample points.

Tap weights are selected to subtract ISI effects from adjacent bits.

Equalized

Equalizer

Desired

Received

R. B. Wu

FIR Filter Design

• Precursor taps: compensate for dispersion-induced phase

distortion, typical requires only single cap.

• Postcursor taps: Compensate for ISI caused by amplitude

distortion. May require multiple taps

• Equalization at driver is often called transmitter emphasis

1

( ) ( )N

n

k

y k c x k n

49

R. B. Wu

Effect of Equalization

50

R. B. Wu

Design Results

51

R. B. Wu

Zero Forcing Solution (ZFS)

• Find pulse response: xi, i=-1, 0, …, N

• Construct output y = X c, i.e.,

• Requiring ytarget=[0, 1, 0, …, 0]T to solve

• Normalized such that

0 1 1

1 1 0

2 1 0 1 1

2 1 0 2( 2)

0 0

0; ;

o

N

x x c

x x x c

x x x x c

x x x c

cy Xc X

1

target ;ZFS

c X y

1

1N

i

i

c

52

R. B. Wu

• The receive-side DLE

works just like the

transmitter pre-

emphasis circuit.

• The only difference is

that it samples the

incoming analog

voltage.

• Uses a “sample & hold”

circuit at the input,

which provides the input

signal stream to the FIR.

C

-1C

0C

1C

2

D D D

S y

k

x

k

Receiver DLE

53

R. B. Wu

Non-idealities in DLE’s

• Practical DLE implementation has limited resolution on

tap coefficients.

• 3-digit resolution would entail suing a 10-bit binary digital

to analog converters.

• Real example: 6-bit DAC for a four-tap equalizer that

achieve 8 Gbps over a 102 cm PCB-based channel.

• Other non-idealities include error in sampled data due to

jitter, quantization noise of DAC, nonlinearity of equalizer

tap and summing circuits, etc.

• DLEs do not improve signal/noise ratio. The performance

gain is due to the increase in usable bandwidth by

flattening frequency response.

54

R. B. Wu

Decision Feedback Equalizer (DFE)

55

R. B. Wu

Decision Feedback Equalizers

Characteristics:

• No noise enhancement

– Input to FBF has no noise, as opposed to DLE input.

• Assumes all past decisions are correct

– Erroneous decisions corrupt future decisions.

– There are coding methods to minimize impact.

• Corrects for only post-cursor ISI

h(t) Sr(t)

Channel n(t)

t=0 ykxk

FBF

S

Bit slicer

56

R. B. Wu

DFE Operation

• The DFE uses the same FIR filter structure as the DLE.

• The input signal is summed with the feedback signal to provide input to a bit

slicer, which decodes the signal into either a “1” or a “0”.

• The output from the bit slicer is used as input to the FIR filter.

C-N

C-N+1

CN-1

CN

T T T T

S

in S out

Feedback

Filter

0 1 2 3 4 5 6 7 850

10

70

130

190

250

310

370

430

490

550

time [ns]

vo

lta

ge

[mV

]

x

0 1 2 3 4 5 6 7 850

0

50

100

150

200

250

300

350

400

450

time [ns]

vo

lta

ge

[mV

]

x

R. B. Wu

20 10 0 10 20 30 40 50 60 70 80 90 100 110 120150

120

90

60

30

0

30

60

90

120

Worst Case Received Eyes

time [ps]

vo

ltag

e (

mV

)

DFE OperationN

o E

QD

LE

DL

E +

DF

E

0 1 2 3 4 5 6 7 8 9 10300

250

200

150

100

50

0

50

100

time (ns)

dif

fere

nti

al v

olt

age

[V]

0 1 2 3 4 5 6 7 8 9 10300

250

200

150

100

50

0

50

100

time (ns)

dif

fere

nti

al v

olt

age

[V]

0 1 2 3 4 5 6 7 8 9 10300

250

200

150

100

50

0

50

100

time (ns)

dif

fere

nti

al v

olt

age

[V]

76 ps

89 ps

96

mV

90

mV

The DFE requires an open eye, so it is typically used with a linear equalizer on the front end.

58

R. B. Wu

Adaptive Equalization

• Ideally, tap coefficients are

tuned to each system to

account for operational (V, T)

and manufacturing variation.

• This is done using adaptive

algorithms.

• Perfect adaptation isn’t

practical.

–Limited by things like

update rate, coefficient

resolution, etc.

C-N

C-N+1

CN-1

CN

D D D D

S

xk

Coefficient Adjustment

S

C-N

C-N+1

CN-1

CN

T T T T

S yk

xk

Coefficient Adjustment

Adaptive DLE

Adaptive DFE

R. B. Wu

Crosstalk Cancellation

• Some noise sources can be compensated (some can’t).

• A simple way to cancel the effects of crosstalk is shown below

(Zerbe 2001).

Transmit

Filter

ht(t)

Receiving

Filter

hr(t)

S

AWGN

n(t)

{xk}

r(t)Channel

hc(t)

T T

t = kT

Detector {xk}

tnthththtxth rcts

XTC

SS1EQX1A

EQX1B

XTC

SS2EQX2A

EQX2B

XTCS3EQX3A

EQX3B

S

Operation:

XTC samples outgoing data is &

multiplies it with a tap weight over a unit

interval.

The weighted signal is sent to the

adjacent signal on each side, where it is

summed with the outgoing data.

60

R. B. Wu

Summary

• Channels act as filters that cause both amplitude and phase

distortion of signals.

• Transmitters and receivers can be designed as filters to

compensate for non-ideal channel behavior.

• Discrete linear equalizers at the transmitter and receiver are

seeing wide use for multi-Gb/s signaling.

• Multiple techniques are available for setting filter tap weights.

• Crosstalk can be cancelled, too.

61

R. B. Wu

References

• S. Hall and H. Heck, Advanced Signal Integrity for High Speed Digital Designs, John Wiley & Sons, 2009.

• L. Couch, Digital and Analog Communication Systems, 2nd edition, MacMillan, New York, 1987.

• W.J. Dally and J. Poulton, “Transmitter equalization for 4-Gbps signaling,” IEEE Micro, Jan./Feb. 1997, pp. 48-56.

• J. Jaussi, et. al., “8-Gb/s source-synchronous I/O links with adaptive receiver equalization, offset cancellation, and clock de-skew,” IEEE J-SSC, Vol. 40, Jan. 2005, pp. 80-88.

• R. Sun, J. Park, F. O’Mahony, and C. P. Yue, “A low-power, 20-Gb/s continuous-time adaptive passive equalizer,” IEEE ICAS 2005, pp. 920-923.

• J. Liu and X. Ling, “Equalization in high-speed communication systems,” IEEE CS Mag., Vol. 4, 2004, pp. 4-17.

• R. Lucky, “The adaptive equalizer,” IEEE SP Mag., 2006, pp. 104-107.

• S. Qureshi, “Adaptive equalization,” Proc. IEEE, Vol. 73, No. 9, Sept. 1985, pp. 1349-1387.

62

R. B. Wu

References

• H. Kim, et al., "A wideband on-interposer passive equalizer design for

chip-to-chip 30-Gb/s serial data transmission," IEEE T-CPMT, 2015.

• Y.-J. Cheng, et al., "Novel differential-mode equalizer with broadband

common-mode filtering for Gb/s differential-signal transmission,"

IEEE T-CPMT, 2013.

• M. Shin, et al., "Small-size low-cost wideband continuous-time linear

passive equalizer with an embedded Cavity structure on a high-speed

digital channel," IEEE T-CPMT, 2014.

• C.-C. Chou, …, T.-L. Wu, "Estimation method for statistical eye

diagram in a nonlinear digital channel," IEEE T-EMC, 2015.

• K.-Y. Yang, …, R.-B. Wu, "Modeling and fast eye diagram estimation

of ringing effects on branch line structures," IEEE T-CPMT, 2014.

• S.-Y. Huang, …, R.-B. Wu, "Fast prediction and optimal design for

eye-height performance of mismatched transmission lines," IEEE T-

CPMT, 2014.63

R. B. Wu

Homework

• Exercises 12-2, 12-3, 12-6, 12-7

64